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Finite Sample Identification of Wide Shallow Neural Networks with Biases
Artificial neural networks are functions depending on a finite number of parameters typically encoded as weights and biases.
Stable Recovery of Entangled Weights: Towards Robust Identification of Deep Neural Networks from Minimal Samples
In this paper we approach the problem of unique and stable identifiability of generic deep artificial neural networks with pyramidal shape and smooth activation functions from a finite number of input-output samples.
Robust and Resource Efficient Identification of Two Hidden Layer Neural Networks
Gathering several approximate Hessians allows reliably to approximate the matrix subspace $\mathcal W$ spanned by symmetric tensors $a_1 \otimes a_1 ,\dots, a_{m_0}\otimes a_{m_0}$ formed by weights of the first layer together with the entangled symmetric tensors $v_1 \otimes v_1 ,\dots, v_{m_1}\otimes v_{m_1}$, formed by suitable combinations of the weights of the first and second layer as $v_\ell=A G_0 b_\ell/\|A G_0 b_\ell\|_2$, $\ell \in [m_1]$, for a diagonal matrix $G_0$ depending on the activation functions of the first layer.
